High quality vanadium dioxide films

ABSTRACT

Layers of high quality VO 2  and methods of fabricating the layers of VO 2  are provided. The layers are composed of a plurality of connected crystalline VO 2  domains having the same crystal structure and the same epitaxial orientation.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of U.S. patent application Ser. No. 14/974,178 that was filed Dec. 18, 2015, the entire contents of which are hereby incorporated by reference.

REFERENCE TO GOVERNMENT RIGHTS

This invention was made with government support under N00014-13-1-0183 awarded by the United States Navy. The government has certain rights in the invention.

BACKGROUND

VO₂ is a fascinating correlated-oxide material that possesses strong coupling among its charge, spin, orbital, and lattice degrees of freedom. VO₂ exhibits a sharp metal-insulator transition (MIT) above room temperature (i.e., transition temperature T_(MIT) of ˜341 K in bulk) with an accompanying structural-phase transition from high-temperature rutile to low-temperature monoclinic structures. This unique property coupled with an almost five-orders-of-magnitude conductivity change (in single-crystal bulks) across the transition make VO₂ a compelling model system for scientific and technological endeavors. Furthermore, the ultrafast nature of VO₂'s MIT gives it diverse potential applications in materials physics and solid-state electronics. Critical to any practical application for VO₂, as well as to exploration of its fundamental physics, is the ability to grow high-quality epitaxial thin films.

Yet it has been difficult to achieve heteroepitaxy in VO₂ thin films due to several intrinsic problems that hamper reliable and predictable VO₂ device performance. Genuine epitaxial growth without rotational domain variants has been achieved with a TiO₂ substrate, owing to the rutile, isostructural symmetry between VO₂ and TiO₂ at their respective growth temperatures. Despite structural compatibility, though, there is a slight lattice mismatch of ˜1.0% between VO₂ and TiO₂, causing a gradual strain relaxation when a film's thickness exceeds a critical value (i.e., ˜20 nm), and this results in severe inhomogeneities throughout the films and in a broad MIT. Even worse, this strain relaxation is accompanied by the formation of cracks that degrade VO₂'s MIT features, including its magnitude of resistance change across the MIT.

SUMMARY

Layered oxide structures comprising an overlayer of high quality VO₂ and methods of fabricating the layered oxide structures are provided. Also provided are high-speed switches comprising the layered structures and methods of operating the high-speed switches.

One embodiment of a layered oxide structure comprises: (a) a substrate comprising single-crystalline TiO₂; (b) an intervening layer comprising columnar, crystalline domains of rutile SnO₂ on the substrate, wherein the columnar, crystalline domains of SnO₂ have an epitaxial relationship with the single-crystalline TiO₂; and (c) an overlayer comprising crystalline domains of VO₂ on the intervening layer, wherein the crystalline domains of VO₂ have an epitaxial relationship with the columnar, crystalline domains of rutile SnO₂. In the structure, the VO₂ has a metal-insulator phase transition critical temperature, below which the VO₂ has a monoclinic crystal structure and above which the VO₂ has a rutile crystal structure.

One embodiment of a switch comprises: a body comprising: (a) a substrate comprising single-crystalline TiO₂; (b) an intervening layer comprising columnar, crystalline domains of rutile SnO₂, wherein the columnar, crystalline domains of SnO₂ have an epitaxial relationship with the single-crystalline TiO₂; and (c) a channel layer comprising crystalline domains of VO₂ on the intervening layer, wherein the crystalline domains of VO₂ have an epitaxial relationship with the columnar, crystalline domains of rutile SnO₂. The VO₂ of the channel has a metal-insulator phase transition critical temperature, below which the VO₂ has a monoclinic crystal structure and above which the VO₂ has a rutile crystal structure. The switch also includes: (d) a first electrically conducting contact in electrical communication with a first area of the channel layer; (e) a second electrically conducting contact in electrical communication with a second area of the channel layer; and (f) an external stimulus source, such as an external voltage source, configured to apply a metal-insulator phase transition-inducing external stimulus to the channel layer.

One embodiment of a method for operating the switch comprises: applying an external voltage from an external voltage source to the first electrically conducting contact, wherein the external voltage induces the VO₂ to undergo a phase transition from the electrically insulating monoclinic crystal structure to the electrically conducting rutile crystal structure.

The switch can be a field effect switch comprising: a body comprising: (a) a substrate comprising single-crystalline TiO₂; (b) an intervening layer comprising columnar, crystalline domains of rutile SnO₂, wherein the columnar, crystalline domains of SnO₂ have an epitaxial relationship with the single-crystalline TiO₂; and (c) a channel layer comprising crystalline domains of VO₂ on the intervening layer, wherein the crystalline domains of VO₂ have an epitaxial relationship with the columnar, crystalline domains of rutile SnO₂. The VO₂ of the channel has a metal-insulator phase transition critical temperature, below which the VO₂ has a monoclinic crystal structure and above which the VO₂ has a rutile crystal structure. The field effect switch further includes: (d) a source; (e) a drain, wherein the source and drain are connected by the channel layer; (f) a gate stack comprising: a gate oxide on the channel layer and a gate contact on the gate oxide; and (g) an external voltage source configured to apply a metal-insulator phase transition-inducing external voltage to the gate contact.

One embodiment of a method for operating the field effect switch comprises: applying a gate voltage from the external voltage source to the gate contact, wherein the external voltage induces the VO₂ to undergo a phase transition from the electrically insulating monoclinic crystal structure to the electrically conducting rutile crystal structure.

One embodiment of a method of making a layered oxide structure comprises: epitaxially growing a layer of columnar, crystalline domains of rutile SnO₂, on a substrate comprising single-crystalline TiO₂; and epitaxially growing an overlayer comprising crystalline domains of VO₂ on the layer of columnar, crystalline domains of rutile SnO₂.

Other principal features and advantages of the invention will become apparent to those skilled in the art upon review of the following drawings, the detailed description, and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Illustrative embodiments of the invention will hereafter be described with reference to the accompanying drawings, wherein like numerals denote like elements.

FIG. 1. Schematic diagram showing a multilayered structure comprising a VO₂ overlayer below its critical phase transition temperature (right) and above its critical phase transition temperature (left). The rutile (left) and monoclinic (right) crystal structures of the VO₂ are shows above the multilayered structures.

FIG. 2. TEM of a multilayered structure comprising a VO₂ overlayer below its critical phase transition temperature, with different rotational orientations of the VO₂ domains indicated.

FIG. 3. Schematic diagram of a two-terminal switch with a VO₂ channel layer.

FIG. 4. Schematic diagram of a three-terminal switch with a VO₂ channel layer.

FIG. 5A. Atomic structures of rutile, metallic VO₂ (upper left); monoclinic, insulating VO₂ (upper right); rutile TiO₂ (lower left); and rutile SnO₂ (lower right) (corresponding lattice parameters are also shown). FIG. 5B. Schematic diagram showing the expected lattice-strain profiles for epitaxial VO₂ films on TiO₂ without a SnO₂ template. FIG. 5C. Schematic diagram showing the expected lattice-strain profiles for epitaxial VO₂ films on TiO₂ with a SnO₂ template.

FIG. 6A. Monoclinic-to-rutile structural-phase transition upon heating, modeled using in situ TEM measurements of a 300-nm-thick VO₂ film on TiO₂. The phase boundaries between monoclinic and rutile structures at each temperature are represented using solid lines. FIG. 6B. Spatial map of out-of-plane strain ∈_(yy) for VO₂ films on TiO₂. FIG. 6C. Spatial map of electrical potential for VO₂ films on TiO₂. FIG. 6D. Monoclinic-to-rutile structural-phase transition upon heating a 300-nm-thick VO₂ film on an SnO₂-templated TiO₂. FIG. 6E. Monoclinic portion as a function of temperature T, as estimated based on the relative areas of the monoclinic regions in FIGS. 6A and 6D.

FIG. 7A. Resistance R versus temperature T for the VO₂ films of the Example. FIG. 7B. The derivative curves of R for a 300-nm-thick VO₂ film on an SnO₂-templated TiO₂ (closed circles and squares indicate derivatives of the R logarithm, as measured during heating and cooling, respectively; experimental data are fitted using Gaussian curves [solid lines]). FIG. 7C. Refractive index n as function of temperature and λ for the 300-nm-thick VO₂/SnO₂/TiO₂ film. FIG. 7D. Extinction coefficient k as function of temperature and λ, for the 300-nm-thick VO₂/SnO₂/TiO₂ film. FIG. 7E. Refractive index n as function of temperature and λ, for the 300-nm-thick VO₂/TiO₂ film. FIG. 7F. Extinction coefficient k as function of temperature and λ, for the 300-nm-thick VO₂/TiO₂ film.

FIG. 8A. Schematic drawing showing strain relaxation and cracking in VO₂ films without SnO₂ templates; in the VO₂ film on an SnO₂-templated TiO₂, severe structural defects, such as strain relaxation and cracks, were well-confined to the interface, and this protects such films against degradation caused by repeated phase transitions. FIG. 8B. Resistance, measured at room temperature and 400 K, after repeated phase transitions of the VO₂ films without SnO₂ templates. FIG. 8C. Schematic drawing showing strain relaxation and cracking in VO₂ films with SnO₂ templates; in the VO₂ film on an SnO₂-templated TiO₂, severe structural defects, such as strain relaxation and cracks, were well-confined to the interface, and this protects such films against degradation caused by repeated phase transitions. FIG. 8D. Resistance, measured at room temperature and 400 K, after repeated phase transitions of the VO₂ films with SnO₂ templates.

FIG. 9A. Microscopic images of the VO₂ films' surfaces for VO₂ grown on TiO₂ (left) and on SnO₂/TiO₂ (right); the image in the inset shows a film surface as observed with a scanning electron microscopy (SEM); prior to SEM imaging, the film surface was chemically etched to observe the resultant cracks more clearly. FIG. 9B. AFM images of the VO₂ films' surfaces for VO₂ grown on TiO₂ (left) and SnO₂/TiO₂ (right).

DETAILED DESCRIPTION

Layered oxide structures comprising an overlayer of high quality VO₂ and methods of fabricating the layered oxide structures are provided. Also provided are high-speed switches comprising the layered structures and methods of operating the high-speed switches.

The layered oxide structures comprise high quality VO₂ epitaxial films grown on a symmetrically isostructural SnO₂ template. The lattice mismatch between the VO₂ and SnO₂ produces small, well-connected domains of VO₂ having the same crystal structure in the epitaxial film and confines severe structural defects (e.g., strain gradients and cracks) to the area near the SnO₂/VO₂ interface. This leads to homogeneous, bulk-like lattices in the VO₂ film, without compromising the film's epitaxial nature. This structural homogeneity also enables homogeneous electronic and chemical states throughout the films, which is highly desirable for creating reliable, high performance devices, such as high-speed switches.

The VO₂ in the epitaxial films is characterized by a metal-insulator phase transition critical temperature. Below this critical temperature, the VO₂ in the epitaxial crystalline domains has an electrically insulating monoclinic crystal structure. As the VO₂ is heated to and above its critical temperature, the crystal structure transitions to a metallic conducting rutile crystal structure. In the VO₂ films, the transition is very sharp and is accompanied by a large decrease in the films' electrical resistance. In addition, the small crystalline domains in the VO₂ films help them to absorb the stresses and strains that accompany the phase transition, enabling the films to undergo many phase transition cycles without cracking. As a result, the VO₂ films are well suited for switching applications. For example, the VO₂ films can be used in electronic switches and optoelectronic switches in circuits, including integrated circuits, for memory devices (e.g., CMOS chips) and communication devices.

One embodiment of a layered structure comprising a VO₂ overlayer is shown schematically in FIG. 1. The right side the figure shows the structure at a first temperature that is below the phase transition critical temperature (T_(crit)) and the left side of the figure shows the structure at a second temperature that is above the T_(crit). The structure comprises a single-crystalline, rutile TiO₂ substrate 102 having an exposed TiO₂ (001) growth surface. A template layer 106 comprising columnar crystalline domains of rutile SnO₂ is disposed on TiO₂ substrate 102. The columnar, crystalline domains of rutile SnO₂ are grown epitaxially and, therefore, have an epitaxially relationship with the underlying TiO₂. Rutile SnO₂ domains have an exposed (001) surface on which an overlayer 110 comprising a plurality of connected crystalline VO₂ domains of is disposed. Epitaxial growth of the SnO₂ and VO₂ can be accomplished using, for example, pulsed laser deposition (PLD) as illustrated in the Example.

The lattice mismatch between the TiO₂ substrate and the SnO₂ results in the epitaxial, nanoscale, crystalline columnar domains in the SnO₂ growing upward from the TiO₂ growth surface. These domains, which have the same crystal structure (rutile) and orientation nucleate separately on the growth surface and grow together to a growth template that is isostructural with the subsequently grown VO₂ at growth temperatures above T_(crit). As such, the SnO₂ films are not polycrystalline films in which a plurality of crystal domains are oriented randomly within the film. As used herein, the term nanoscale columnar domains refers to columnar domains having average cross-sectional diameters that are no greater than 200 nm. This includes columnar domains having average cross-sectional diameters that are no greater than 100 nm; no greater than 50 nm; and no greater than 20 nm. For example, in some embodiments of the SnO₂ films, the columnar domains have average cross-sectional diameters in the range from about 5 nm to about 10 nm. The thickness of the SnO₂ layer is typically in the range from about 100 nm to about 300 nm, but thicknesses outside of this range can be used.

The lattice mismatch between the SnO₂ and the VO₂ limits the size of the epitaxially grown VO₂ domains and concentrates and/or confines any cracks in the VO₂ film to a small volume near the SnO₂/VO₂ interface, while the remainder of the VO₂ may be crack- and strain-free. This is advantageous because it allows the VO₂ layers to be grown to commercially practical thicknesses without any significant cracking beyond the lowermost portion of the layer. By way of illustration only, in some embodiments of the layered structures, the VO₂ layer has a thickness of at least 100 nm. This includes layered structures having a VO₂ layer thicknesses of at least 200 nm and further includes layered structures having a VO₂ layer thicknesses of at least 300 nm. For example, in some embodiments, the VO₂ layer thickness is in the range from about 100 nm to about 500 nm. This includes embodiments in which the VO₂ layer thickness is in the range from about 200 nm to about 400 nm. In each of these embodiments, the cracks and/or strains (if present at all) may be confined to within a few nanometers (for example, 10 nm or fewer, including 5 nm or fewer) of the SnO₂NO₂ interface.

The small size of the VO₂ domains helps the VO₂ film to absorb the stresses and strains of the MIT, which reduces cracking during phase change cycling and improves and sustains device performance. As used here, the size of the domains refers to the largest cross-sectional width of the domains, where the width dimension is perpendicular to the thickness dimension. In some embodiments of the layered structures, the average width of the VO₂ domains is no greater than about 500 nm. This includes embodiments in which the average width of the VO₂ domains is no greater than about 400 nm and further includes embodiments in which the average width of the VO₂ domains is no greater than about 300 nm. The VO₂ domains are well-connected, have a common crystal structure and an epitaxial relationship with the underlying SnO₂. At temperatures below T_(crit), the VO₂ has a monoclinic crystal structure and is electrically insulating. The monoclinic VO₂ domains can have four different rotational orientations that are rotated by 90° from each other in the plane of the film. The different rotational domains are represented by areas of different shading in overlayer 110 on the right side of FIG. 1. The four different rotational domain variants of the monoclinic VO₂ are shown in the upper right side of FIG. 1. At temperatures above T_(crit), the VO₂ has a tetragonal rutile crystal structure and acts as an electrical conductor. The rutile crystal structure is shown in the upper left side of FIG. 1.

The T_(crit) for the VO₂ in the overlayer is greater than room temperature (i.e., greater than 300 K). Typically, the T_(crit) is greater than 340 and in the range from about 338 to about 345 K (e.g., about 340 to 343 K, including about 341 K). (Unless otherwise indicated, the phase transition critical temperatures referred to in this disclosure refer to the critical temperature in the absence of an applied external field or strain.)

The high quality VO₂ films grown on SnO₂ template layers can be characterized by their sharp metal-insulator phase transitions, where the sharpness of a transition is characterized by the full width at half maximum (FWHM) of the derivative curve of a heating curve, as illustrated in the Example. Some embodiments of the VO₂ films have a phase transition sharpness of 2 K or less. This includes VO₂ films having a phase transition sharpness of 1.5 K or less and further includes VO₂ films having a phase transition sharpness of 1 K or less. These sharp transition can be achieved even in films with thicknesses above 100 nm, above 200 nm, and above 300 nm.

The monoclinic to rutile (insulating to conducting) phase transition is accompanied by a large drop in the vanadium dioxide's magnitude of electrical resistance (ΔR), which can be measured as described in the Example. Some embodiments of the VO₂ films have a ΔR of at least 2 orders of magnitude. This includes VO₂ films having a ΔR of at least 3 orders of magnitude and further includes VO₂ films having a ΔR of at least 4 orders of magnitude.

The layered structure can be used as a switch by heating the VO₂ above its T_(crit) to trigger the phase transition. Devices configured to induce or monitor this heating-induced switching can be used as thermal switches and thermal sensors. Alternatively, an external stimulus, such as an electric field, an optical field, a mechanical strain, or a combination thereof, can be applied to the VO₂ to induce the phase transition. These external stimuli shift the critical temperature for the MIT and induce the reversible phase transition, which changes the resistance (and, therefore, conductance) of the VO₂, thereby modulating current flow through the material. Devices configured for field-induced switching can be used as high-speed switches for a variety of electronic, optical, and optoelectronic applications. A basic embodiment of a two-terminal switch comprising the layered structure is shown in the schematic diagram of FIG. 3. This switch is designed to undergo an electric field-induced crystalline phase transition. The switch comprises a channel layer comprising the crystalline domains of VO₂ 302, a first electrically conducting contact 304 in electrical communication with layer 302, and a second electrically conducting contact 306 in electrical communication with layer 302. The switch embodiment shown here also includes a dielectric substrate 307 comprising the SnO₂ 308 and TiO₂ 309 layers of the layered structure. The crystalline phase change in the VO₂ channel layer can be triggered by the application of an external electric field. This is typically accomplished by applying an external voltage from an external voltage source to first electrically conducting contact 304. If the magnitude of the applied voltage is meets a certain voltage threshold, it will induce the phase change and trigger the switch.

FIG. 4 is a schematic diagram of the three-terminal field effect switch that incorporates a VO₂ layer as a channel. The switch comprises a source 412, a drain 414, and a channel layer comprising the crystalline domains of VO₂ 402 disposed between source 412 and drain 414. A gate stack comprising a gate dielectric 416 and a gate contact 418 is disposed on channel layer 402. The field effect switch also includes a dielectric substrate 407 comprising the SnO₂ 408 and TiO₂ 409 layers of the layered structure. The crystalline phase change in the VO₂ channel layer can be triggered by the application of a gate voltage, such as a negative gate voltage, to gate contact 418. If the applied gate voltage is greater than the threshold voltage, it will induce the phase change and trigger the switch.

Although the switches shown in FIGS. 3 and 4 include the SnO₂ template layer and TiO₂ substrate upon which the VO₂ layer is grown, it is also possible to remove one or both of these layers after VO₂ layer growth and then transfer the VO₂ layer onto another support substrate, which may be an electrically conducting (metallic), semiconducting, or electrically insulating substrate.

Example

In this example, VO₂ films were grown on an SnO₂-templated TiO₂ (001) substrate. SnO₂ is insulating and has a rutile symmetry isostructural with VO₂ at its growth temperature, making it relevant as a template for epitaxial VO₂ growth (FIG. 5A). A large lattice mismatch (≥4.2%) between VO₂ and SnO₂ results in an abrupt strain relaxation at the interface region within a few nanometers. As a result, severe structural defects, including strain gradient, were confined only near the interface between the VO₂ and SnO₂, leading to homogeneous, bulk-like lattices in the VO₂ film (FIG. 5C) and a sharp MIT above room temperature. Additionally, the low solid solubility between VO₂ and SnO₂ significantly enhanced the materials' chemical sharpness at the interface by reducing interfacial intermixing. Thus, thin-film epitaxy using an SnO₂ template is a suitable process for producing homogeneous, crystalline, crack-free VO₂ films.

Materials and Methods

Crystalline VO₂ epitaxial thin films were grown on (001) TiO₂ substrates using the pulsed laser deposition (PLD) method. Before deposition, low miscut (<0.1°) TiO₂ substrates were cleaned by sonicating with acetone and then rinsing with isopropanol. An SnO₂ epitaxial layer with a thickness of 100 nm was deposited as a bottom template on the TiO₂ substrate. A KrF excimer laser (λ=248 nm) beam was focused on SnO₂ and V₂O₅ ceramic targets to an energy density of ˜2.0 J/cm² and pulsed at 5 Hz (for SnO₂ layer) or 10 Hz (for VO₂ layer). SnO₂ layers were grown at a substrate temperature of 400° C. and oxygen partial pressure of 50 mTorr. After growth of the SnO₂ layer, the VO₂ layer was grown at the temperature of 400° C. and oxygen partial pressure of 18 mTorr. After growth, the VO₂/SnO₂ films were cooled down to room temperature at an oxygen partial pressure of 18 mTorr.

The structural qualities of the films were examined using high-resolution X-ray diffraction (XRD). The XRD pattern of the VO₂/SnO₂/TiO₂ film showed a clear film peak at 2θ=64.8° along with (002) diffraction peaks from the underlying rutile SnO₂ and TiO₂ substrate. This film peak comes from the ( 4 02) reflection of monoclinic VO₂, and these correspond with the (002) reflection of VO₂'s high-temperature rutile phase. No other peaks were observed using XRD analysis, proving that the VO₂ film was highly oriented and had a pure phase. The peak position (i.e., 2θ=64.7°) was almost identical to that of the ( 4 02) reflection for bulk, monoclinic VO₂, suggesting that the film was fully relaxed and had bulk-like lattices. Importantly, the VO₂/SnO₂/TiO₂ film exhibited a symmetric diffraction peak, well fitted with a single peak, implying that the misfit strain was abruptly relaxed without gradual strain relaxation. In contrast, the VO₂/TiO₂ film exhibited an asymmetrical diffraction peak, implying the presence of a gradual strain relaxation in the film, consistent with this study's initial predictions.

To obtain further information on lattice strains, X-ray reciprocal-space mappings (RSMs) were used. In the case of the VO₂/TiO₂ film, the film's RSM peak position (denoted by a closed, circle) was far from that of the VO₂'s bulk (denoted by a closed, star), indicating that the VO₂ film was still partially strained. Furthermore, the film's RSM peak featured a shoulder directed toward the bulk peak position, confirming gradual strain relaxation in the film. As for the VO₂/SnO₂/TiO₂ film, the peak position of the film was identical to that of the bulk VO₂. This indicates that the use of an SnO₂ template leads to homogeneous lattices, as well as to complete relaxation for the misfit strain in the VO₂ film.

Results

Based on initial predictions, structural inhomogeneity determined the MIT behavior of the VO₂ films. To visualize the role of local inhomogeneities on MIT, in situ transmission electron microscopy (TEM) was used. The monoclinic-to-rutile structural phase transition was monitored by heating the VO₂ films. Abrupt changes to lattice parameters (FIG. 5A), as well as to symmetry, during the phase transition caused noticeable contrast between the monoclinic and rutile regions, allowing clear visualization of the structural phase transition. For VO₂ films on bare TiO₂, the rutile phase started to nucleate from the interface at ˜315 K, which is much lower than the nucleation point for bulk T_(MIT) (i.e., 341 K), and the phase transition was complete near the surface and cracks. The local profile of the films' respective strains and electric potentials were measured using inline holography (FIGS. 6B, 6C), and there was a close relationship between local strain and T_(MIT). However, whereas regions near the surface and cracks experienced negligible strain in the bulk-like T_(MIT), the interfacial regions with relatively more strain preferred the rutile structure and had much lower T_(MIT), resulting in a broad MIT (FIG. 6E).

In contrast, the VO₂ film on SnO₂-templated TiO₂ exhibited a much sharper, bulk-like phase transition and did not exhibit any structural or electronic inhomogeneities distinct from those of the VO₂ film on bare TiO₂. As a result, the VO₂ film on SnO₂/TiO₂ had a much sharper transition, and most of its structural-phase transition was complete between 341 and 343 K (FIGS. 6D, 6E). Interestingly, for the VO₂ film on SnO₂/TiO₂, the structural phase transition began at the surface and ended at the interface, which is the opposite of how the transition progresses in VO₂ films on bare TiO₂ (FIG. 6A). These phase-field simulations reveal that homogeneous VO₂ single crystals have a monoclinic-to-rutile phase transition that begins at the surface. Thus, the present study's in situ TEM and simulation results demonstrate that placing a VO₂ epitaxial film on an SnO₂-templated TiO₂ offers a more reliable, enhanced MIT, whose sharpness and magnitude are as good as those of intrinsic VO₂ single crystals.

To characterize the MIT and its sharpness, electrical resistance was measured as a function of temperature in VO₂ films with or without an SnO₂ template (FIG. 7A). The resistance of the 300-nm-thick VO₂ film on the SnO₂/TiO₂ substrate caused a change of four orders of magnitude (i.e., ≥3×10⁶%) during MIT, while the resistance change was drastically reduced in VO₂ films on bare TiO₂, possibly due to the presence of a strain gradient and cracks (FIGS. 9A and 9B). The transition temperature for the VO₂/SnO₂/TiO₂ film was ˜341 K, the same as for the bulk VO₂. As FIG. 7A also clearly shows, the VO₂/SnO₂/TiO₂ film exhibited a much sharper MIT compared with films of the same thickness on bare TiO₂. The sharpness of the VO₂/SnO₂/TiO₂ film's MIT was quantitatively estimated to be <1 K using the width of its derivative curves (FIG. 7B). This MIT sharpness (i.e., ˜0.5 K) is comparable to that of fully coherent, 10-nm-thick VO₂ films on bare TiO₂. Thus, this study's electrical-transport measurements indicate that homogeneity engineering using an SnO₂ template allows for a sharp, pronounced resistance change across MIT, while maintaining a bulk-like transition temperature.

Thus far, electrical-transport measurements have been used to determine the sharpness of the MIT. However, electrical conduction can be dominated by low-resistive local regions and associated short-circuit currents so that the transport measurements might not effectively reflect MIT sharpness for the overall film region. Because of this, optical measurements were adopted in addition to electrical measurements. Using spectroscopic ellipsometry, refractive index n and extinction coefficient k were measured as a function of temperature. It is known that the complex dielectric function and associated n and k exhibit a noticeable change during MIT. (See, J. B. Kana Kana et al., Opt. Commun. 284, 807 (2011).) Furthermore, in contrast to electrical measurements, measurements of n and k are governed by the averaged optical response for the whole film region, rather than for local regions alone. Thus, optical measurements of n and k effectively reveal genuine MIT features, such as sharpness, in VO₂ films.

FIGS. 7C-F show the values for n and k measured during heating as functions of temperature, as well as wavelength λ of incidental light for 300-nm-thick VO₂ films. For the VO₂/SnO₂/TiO₂ film (FIGS. 3C, 3D), n and k exhibited abrupt changes for every λ across MIT with a T_(MIT) of ˜341 K, and this was the same as with the bulk sample. This sharp transition in n and k is attributable to the film's homogeneous nature (FIG. 5C). And yet, for the VO₂/TiO₂ film (FIGS. 7E, 7F), n and k exhibited gradual changes across MIT with an average T_(MIT) of ˜320 K, and this is attributable to the film's local inhomogeneities (FIG. 5B). Furthermore, the lower average T_(MIT) value compared with the bulk value is attributable to the film's average tensile strain. Thus, these optical measurements confirm that the VO₂/SnO₂/TiO₂ film had a sharp MIT, and they underscore the importance of homogeneity engineering in producing high-quality epitaxial VO₂ films.

Last, SnO₂ template's contributions were examined to prevent the VO₂ from cracking. VO₂ bulk crystals tend to crack under large amounts of stress during MIT, and they degrade upon repeat cycling. Strain relaxation in VO₂ epitaxial films can also cause such cracks (FIG. 8A). In this study, an increasing number of such cracks were formed after repeated thermal cycles, and they severely affected the MIT features of the VO₂ film on bare TiO₂. A more significant, increased resistance to cracks occurred during the nominally metallic phase, and as a result, the magnitude of resistance change across the MIT was far less, down to ˜10⁵%. On the other hand, the VO₂ films on SnO₂/TiO₂ had robust MITs, and the magnitude of their resistance change remained at ˜10⁶%, even after 1,000 cycles. This indicates that, once confined to the interface, structural defects like cracks don't spread into the films after repeated cycles with VO₂/SnO₂/TiO₂ films.

This example demonstrates thin-film epitaxy of structurally homogeneous, crack-free VO₂ with a sharp, reliable MIT grown using an SnO₂ template layer. Furthermore, correlated electron materials have exhibited various other novel phenomena in addition to the MIT, including superconductivity and colossal magnetoresistance—both of which are desirable for emerging electronics applications. These properties are, generally, strongly dependent on lattice strain due to a combination of charge, spin, orbitals, and degrees of lattice freedom. Thus, this study provides a general framework for predictively designing homogenous, heteroepitaxial materials with reliable electronic functions that include, but are not limited to, material MIT.

The word “illustrative” is used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as “illustrative” is not necessarily to be construed as preferred or advantageous over other aspects or designs. Further, for the purposes of this disclosure and unless otherwise specified, “a” or “an” means “one or more”.

The foregoing description of illustrative embodiments of the invention has been presented for purposes of illustration and of description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and modifications and variations are possible in light of the above teachings or may be acquired from practice of the invention. The embodiments were chosen and described in order to explain the principles of the invention and as practical applications of the invention to enable one skilled in the art to utilize the invention in various embodiments and with various modifications as suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto and their equivalents. 

What is claimed is:
 1. A layer of VO₂ comprising a plurality of connected crystalline VO₂ domains having the same crystal structure and the same epitaxial orientation, wherein the layer of VO₂ is a continuous layer in which the crystalline VO₂ domains in the plurality of connected crystalline VO₂ domains are in direct contact with other crystalline VO₂ domains in the plurality of crystalline VO₂ domains.
 2. The layer of VO₂ of claim 1, wherein the layer is crack free.
 3. The layer of VO₂ of claim 1, wherein the layer is strain free.
 4. The layer of VO₂ of claim 1, having a layer thickness of at least 100 nm.
 5. The layer of VO₂ of claim 4, having a layer thickness in the range from 100 nm to 500 nm.
 6. The layer of VO₂ of claim 4, wherein any cracks present in the layer are confined to within 10 nm or fewer of one surface of the layer.
 7. The layer of VO₂ of claim 4, wherein any strain present in the layer is confined to within 10 nm or fewer of one surface of the layer.
 8. The layer of VO₂ of claim 4, wherein the crystalline VO₂ domains have an average width of no greater than 500 nm and any cracks present in the layer are confined to within 5 nm or fewer of one surface of the layer.
 9. The layer of VO₂ of claim 1, wherein the crystalline VO₂ domains have an average width of no greater than 500 nm.
 10. The layer of VO₂ of claim 1, wherein the crystalline VO₂ domains have an average width of no greater than 300 nm.
 11. The layer of VO₂ of claim 1, wherein the VO₂ has a metal-insulator phase transition critical temperature, below which the VO₂ has a monoclinic crystal structure and above which the VO₂ has a rutile crystal structure, the layer of VO₂ being characterized in that, when it is heated from a temperature below its metal-insulator phase transition critical temperature to a temperature above its metal-insulator phase transition critical temperature, the VO₂ undergoes the phase transition from monoclinic to rutile with a transition sharpness of no greater than 2 K.
 12. The layer of VO₂ of claim 11, wherein the VO₂ has a metal-insulator phase transition critical temperature, below which the VO₂ has a monoclinic crystal structure and above which the VO₂ has a rutile crystal structure, the layer of VO₂ being characterized in that, when it is heated from a temperature below its metal-insulator phase transition critical temperature to a temperature above its metal-insulator phase transition critical temperature, the VO₂ undergoes a phase transition from monoclinic to rutile and the electrical resistance of the layer of VO₂ decreases by at least four orders of magnitude.
 13. The layer of VO₂ of claim 1, wherein the VO₂ has a metal-insulator phase transition critical temperature, below which the VO₂ has a monoclinic crystal structure and above which the VO₂ has a rutile crystal structure, the layer of VO₂ being characterized in that, when it is heated from a temperature below its metal-insulator phase transition critical temperature to a temperature above its metal-insulator phase transition critical temperature, the VO₂ undergoes the phase transition from monoclinic to rutile with a transition sharpness of no greater than 1 K.
 14. The layer of VO₂ of claim 1, wherein the VO₂ has a metal-insulator phase transition critical temperature, below which the VO₂ has a monoclinic crystal structure and above which the VO₂ has a rutile crystal structure, the layer of VO₂ being characterized in that, when it is heated from a temperature below its metal-insulator phase transition critical temperature to a temperature above its metal-insulator phase transition critical temperature, the VO₂ undergoes a phase transition from monoclinic to rutile and the electrical resistance of the layer of VO₂ decreases by at least four orders of magnitude.
 15. The layer of VO₂ of claim 1, wherein the layer overlies a template layer with which the VO₂ has a lattice mismatch.
 16. The layer of VO₂ of claim 1, wherein layer of VO₂ overlies a layer of columnar, crystalline domains of rutile SnO₂.
 17. The layer of VO₂ of claim 1, wherein the plurality of connected crystalline VO₂ domains includes crystalline VO₂ domains having different rotational orientations. 